The shape of the Universe is an informal name for a subject of investigation within physical cosmology which describes the geometry of the universe including both local geometry and global geometry. It is loosely divided into curvature and topology, even though strictly speaking, it goes beyond both. More formally, the subject in practice investigates which 3-manifold corresponds to the spatial section in comoving coordinates of the 4-dimensional space-time of the Universe.
Within the Friedmann-Lemaître-Robertson-Walker (FLRW) model, the presently most popular shape of the Universe found to fit observational data according to cosmologists is the infinite flat model, while other FLRW models that fit the data include the Poincaré dodecahedral space  and the Picard horn.
Considerations of the shape of the universe can be split into two parts; the local geometry relates especially to the curvature of the universe at points everywhere, and especially in the observable universe, while the global geometry relates especially to the topology of the universe as a whole — which may or may not be within our ability to measure.
Cosmologists normally work with a given space-like slice of spacetime called the comoving coordinates. In terms of observation, the section of spacetime that can be observed is the backward light cone (points within the cosmic light horizon, given time to reach a given observer). For related issues, see distance measures (cosmology). The related term Hubble volume can be used to describe either the past light cone or comoving space up to the surface of last scattering. From the point of view of special relativity alone, speaking of "the shape of the universe (at a point in time)" is ontologically naive because of the issue of relativity of simultaneity: you cannot speak of different points in space being "at the same point in time", thus you cannot speak of "the shape of the universe at some point in time". However, the existence of a preferred set of comoving coordinates is possible and widely accepted in present-day physical cosmology.
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